I think they can have both: Ego Draconis did it pretty well, having a number of random, odd and absurd touches, be it the handstand at the apex of a ladder or the hermit-with-the-wit-of-a-carrot, or the Broken Valley Village gossips, or the gravestones, or the Horror of High Hall's exclamation of "oh bugger!"... etc. But I don't think it detracted at all from what was actually quite a serious storyline, and something which I found to be quite heart-rending more than once.
Perhaps it reflects our own approach to life: I've often been told off for not being as serious as a situation dictated, sometimes in an official capacity, but personally I felt my misbehaviour just added character and general seasoning to something that needed a bit more depth. Well okay, perhaps "need" is going a bit far, but y'know.
Do you see what you're doing though? You're naming things that meshed with the silly animations, things that reinforced it in the world. In this game the animations are alone in a world that doesn't support them. I'm sure there are ways to pull off a very serious and also very silly story, but even then it hints at some kind of insanity on the part of the story teller. (Which would be the player character, in Divinity's case.)
What kind of character would
always perform an acrobatic trick at the top of a ladder? In a world like this, that character would be a sociopath, because with all these awful things happening and the somber mood they would have to be seriously disconnected from any kind of normal range of emotions or feeling of community to do something like that. If this really, really must be kept in the game the way the story is now, then it would have to be in the form of a tag added for "Lunatic", so that when you have both "Lunatic" and "Jester" you will perform acrobatic tricks.
Whatever form it comes in, unless the story is planning to be changed drastically, it should be reserved to an option.